Two exemplary modem communication systems which permit transmission of data over band-limited communication lines at very high rates (e.g., up to 52 Mbits/s) are the asymmetric high speed digital subscriber line (ADSL) and very high speed digital subscriber line (VDSL) systems. Further information on these system may be found in “ADSL, VDSL and Multi-carrier Modulation”, J. A. C. Bingham, Wiley, 2000.
More particularly, the above-noted systems are examples of multi-carrier systems. Multi-carrier modulation is one way of transmitting digital data by splitting that data into fixed-length data “blocks” or “symbols,” each having the same number of sub-blocks or bits. Analog transmission of these blocks is carried out using a set of carrier signals. There is a carrier for each of the sub-blocks in one block. The carriers have frequencies which are equally spaced across the transmission band of the transceiver. One such arrangement is called discrete multi-tone (DMT). DMT modems transmit data by dividing it into several interleaved bit streams, and these bit streams are used to modulate several carriers.
Another application of multi-carrier modulation is in orthogonal frequency division multiplexing (OFDM) systems, as described in “OFDM for Wireless Multimedia Communications”, R. van Nee and R. Prasad, Artech House, 2000, for example. This modulation technique finds application in wireless local area networks (WLAN), as well as in satellite communications. See, e.g., “Satellite Communications Systems”, G. Maral, M. Bousquet, Wiley, 1998.
By way of example, in a receiver for use in an ADSL system, following time domain equalization (TEQ), a removal of the cyclic prefix (CP) and a fast Fourier transform (FFT) (which is complementary to the inverse FFT (IFFT) of the transmitter) is performed. The signal may then be passed to a frequency domain equalizer (FDEQ) to recover the transmitted signals from the received signals (e.g., QAM symbols), from which the bit streams are recovered.
A significant drawback of this and other multiple carrier systems is the effect of clock offset on performance. ADSL standards require that client-side modems recover a master clock signal from the received data stream, and use this recovered clock to generate a jitter-free reverse link bitstream. This is done to ensure that the upstream transmission is received by the central office modem in a synchronized manner relative to the master clock signal.
Clock offset in the transmission path introduces a tone-dependent frequency shift and a sample-dependent time delay. It is conventionally addressed by carrying out a time domain interpolation (TDI) at the customer premises equipment (CPE) only for ADSL. The Central Office (CO) is the master and usually does not need TDI, but this is optional. The TDI is used to pre-compensate signals transmitted to, and post-compensate signals received from, the CPE side. Conventionally, this involves a polynomial (Lagrange) interpolation. See, e.g., “The Theory and Practice of Modem Design”, J. A. C. Bingham, Wiley, 1988.
A definition of interpolation given in the foregoing book which is as follows: “given a set of M values Fm with m=1 to M of a function F(t) generated by sampling at equally spaced values tm of time t, find an approximation to F(t) for t lying within the range of tm.” The simplest solution is to fit a polynomial of degree M−1 through the observed values of F(t). The offset is typically a very small proportion of the clock period, but very small uncorrected offsets have a disproportional effect on subsequent processing stages. This is because in a multi-carrier system SNR will drop dramatically due to ICI resulting from FFT of signals having any clock offset. Thus, as a polynomial fit is only an approximation to the actual signal, errors are automatically introduced because of the inaccurate fit between the polynomial approximation and the real signal.
The known TDI structure can be replicated in the transmitter (TX) for pre-compensation, using the same TDI structure used in the receiver. However, the TDI in the TX path may introduce noise at high frequency and non-linear behavior due to polynomial (Lagrange) interpolation which, in turn, may affect the performance of the local echo canceller and the remote channel equalizer. Also, it may be very expensive in terms of required computation.
U.S. Pat. No. 6,370,188 to Wu et al. discusses phase and frequency offset compensation in a telecommunications receiver. A pre-emphasis FIR filter function and a pre-emphasis phase rotation function are applied to an upstream signal, based upon the estimated phase offset and frequency offset. A transmit side includes an FIR filter function which receives a digital signal G(m), directly or indirectly, from a host computer. The FIR filter applies a pre-emphasis correction to the signal G(m), based upon the estimate of frequency offset between the master clock of a central office modem 100 and a receive clock. This frequency offset estimate is communicated to the FIR filter function by a phase and frequency offset detection function. This is an example of a polynomial type correction.
U.S. Pat. No. 6,101,230 to Chun et al. is directed to sampling clock signal recovery in a receiving terminal of a DMT system, in which additive white Gaussian noise (AWGN) induced jitter is a problem. To address this problem, the patent proposes removing AWGN from the receiving terminal of the DMT system, and stably recovering a sampling clock signal by first determining whether the phase error is smaller than a predetermined threshold value. If the phase error is equal to, or greater than the predetermined threshold value, then it corrects the sampling clock signal by the phase error. However, if the phase error is less than the predetermined threshold value, then it calculates an average value of some or all of decision error values, and corrects the sampling clock signal by the average value.
Published U.S. Patent application no. 2001/0019593 A1 to Greaves, David J. describes an xDSL sample rate compensation approach using phase balancing. It compares the local sampling rate with the reference sampling rate, determines the error in the local sample rate, and derives a timing recovery signal related to the magnitude of the error. It further divides the local clock rate by a factor related to the timing recovery signal to reduce the error. One or more samples is removed from or added to the received sample stream, at predetermined intervals, depending on the timing recovery signal to further reduce the error.